GATE 2025 ST – Question 65

Multivariate Analysis · Multivariate Normal and Wishart Distributions · 2 marks · Numerical answer

Bivariate normal X,Y have means 2,3,variances 16,25 and covariance 14. Find 2π[P(X>2,Y>3)−1/4] to two decimals.

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Correct answer: 0.75 to 0.80

Explanation

The standardized correlation is ρ=14/(4·5)=.7. For a centered standard bivariate normal, the positive-orthant probability is 1/4+arcsinρ/(2π), obtained from the angular sector of two independent standard-normal coordinates. The requested expression is therefore arcsin(.7)≈**.78 radians**.

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